Starting a new standard game, a player must choose between easy, normal, veteran, and elite modes. After beating the final boss, you can start New Game Plus. Are there also 4 difficulty levels for New Game Plus? If so, do you choose the difficulty again or does it carry over from your character's last game?

2 Answers
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Upon accepting and finishing the quest that gives you NG+, you will be booted back to the initial character loading screen (where you can switch between characters etc.).

You can then choose to Resume to play on your character, that is now in NG+ mode.
This means its level will remain the same, aswell as the skills and stats.
All your progress however is lost, so you start with a new world and the same quests you did before. You do however still have access to the Mapworks by using any Waypoint Portal.

You are not prompted to change the difficulty mode at any time (a pity in my eyes), so your difficulty setting is carried over.

You can ofcourse always change the difficulty setting if you want, as explained in this post.